Which of the following numbers is a factor of 42? ${4,5,9,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $42$ by each of our answer choices. $42 \div 4 = 10\text{ R }2$ $42 \div 5 = 8\text{ R }2$ $42 \div 9 = 4\text{ R }6$ $42 \div 13 = 3\text{ R }3$ $42 \div 14 = 3$ The only answer choice that divides into $42$ with no remainder is $14$ $ 3$ $14$ $42$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $14$ are contained within the prime factors of $42$ $42 = 2\times3\times7 14 = 2\times7$ Therefore the only factor of $42$ out of our choices is $14$. We can say that $42$ is divisible by $14$.